In my opinion the most beautiful scenery between Washington and southern Florida is along Skyline Drive, the Blue Ridge Parkway and Great Smokies Mountains National Park. The Outer Banks of North Carolina would probably be my second choice. Yes, there are lots of other beautiful beaches in the Southeast, but the drives to get to those beaches (other than the Outer Banks) aren't particularly scenic.
Since you're going to fly out of Miami, I second your choice to explore the Keys. I would also recommend the Everglades.

Of course, given your time frame, you definitely don't have enough time to see all I would recommend. Given that you'll be traveling in November after the fall foliage has dropped in the mountains, you probably should consider one of these alternatives;
1- Take the Skyline Drive through the Shenandoahs and the Blue Ridge Parkway down to southern Virginia for 2 or 3 days. Then take I-77 south to I-26 east to I-95 south. Then explore some beaches in Georgia and Florida.
or
2- Take I-81 south to I-26 east to the Asheville area. Then explore Asheville, the southern portion of the Blue Ridge Parkway and the Smokies for 3-4 days. Then take I-75 south through Georgia and then down the west coast of Florida to the Everglades and the Keys.